Theorem bj-alalbial 37051

Description: Adding a second quantifier over the same variable is a transparent operation, (∀∀ case). (Contributed by BJ, 20-Oct-2019.)

Assertion

Ref	Expression
bj-alalbial	⊢ (∀𝑥∀𝑥𝜑 ↔ ∀𝑥𝜑)

Proof of Theorem bj-alalbial

Step	Hyp	Ref	Expression
1		nfa1 2162	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	19.3 2214	1 ⊢ (∀𝑥∀𝑥𝜑 ↔ ∀𝑥𝜑)

Syntax hints:   ↔ wb 207  ∀wal 1545

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-10 2152  ax-12 2189

This theorem depends on definitions:  df-bi 208  df-or 854  df-ex 1787  df-nf 1791

This theorem is referenced by: (None)